We prove that every smooth Fano complete intersection of index and codimension in is birationally superrigid and K-stable if . We also propose a generalization of Tian’s criterion of K-stability and, as an application, prove the K-stability of the complete intersection of a quadric and a cubic in . In the appendix (written jointly with C. Stibitz), we prove the conditional birational superrigidity of Fano complete intersections of higher index in large dimension.
"Birational superrigidity and K-stability of Fano complete intersections of index ." Duke Math. J. 169 (12) 2205 - 2229, 1 September 2020. https://doi.org/10.1215/00127094-2020-0010